Chapter 8

In \(3-14,\) solve each equation for the variable. Express each answer to the nearest hundredth. $$ 7\left(2^{b}\right)=815 $$

Solve each equation for the variable and check. \(\log 8-\log x=\log 2\)

In \(3-14,\) write each exponential equation in logarithmic form. $$ 5^{-3}=0.008 $$

In \(3-14,\) find the common logarithm of each number to the nearest hundredth. $$ 0.342 $$

\(\ln 3-10 :\) a. For each \(f(x),\) write an equation for \(f^{-1}(x),\) the inverse function. b. Sketch the graph of \(f(x)\) and of \(f^{-1}(x) .\) $$ f(x)=\frac{1}{3^{x}} $$

In \(3-14,\) find the natural logarithm of each number to the nearest hundredth. $$ 0.0759 $$

In \(3-14,\) solve each equation for the variable. Express each answer to the nearest hundredth. $$ 5\left(10^{y}\right)=1,200 $$

Solve each equation for the variable and check. \(\log (x+3)=\log (x-5)+\log 3\)

In \(3-14,\) write each exponential equation in logarithmic form. $$ 4^{-2}=0.0625 $$

In \(3-14,\) find the common logarithm of each number to the nearest hundredth. $$ 0.0759 $$

\(\ln 3-10 :\) a. For each \(f(x),\) write an equation for \(f^{-1}(x),\) the inverse function. b. Sketch the graph of \(f(x)\) and of \(f^{-1}(x) .\) $$ f(x)=-2^{x} $$

In \(3-14,\) find the natural logarithm of each number to the nearest hundredth. $$ 1 $$

In \(3-14,\) solve each equation for the variable. Express each answer to the nearest hundredth. $$ (2 \times 8)^{x}=0.25 $$

Solve each equation for the variable and check. \(\log x+\log (x+7)=\log 30\)

In \(3-14,\) write each exponential equation in logarithmic form. $$ 7^{-1}=\frac{1}{7} $$

In \(11-22,\) solve each equation for \(y\) in terms of \(x\) $$ x=6^{y} $$

In \(3-14,\) find the natural logarithm of each number to the nearest hundredth. $$ e $$

In \(3-14,\) solve each equation for the variable. Express each answer to the nearest hundredth. $$ (5 \times 7)^{a}=0.585 $$

Solve each equation for the variable and check. \(\log x+\log (x-1)=\log 12\)

In \(3-14,\) write each exponential equation in logarithmic form. $$ 64^{\frac{1}{3}}=4 $$

In \(3-14,\) find the common logarithm of each number to the nearest hundredth. $$ 10 $$

In \(11-22,\) solve each equation for \(y\) in terms of \(x\) $$ x=10^{y} $$

In \(3-14,\) find the natural logarithm of each number to the nearest hundredth. $$ e^{2} $$

In \(3-14,\) solve each equation for the variable. Express each answer to the nearest hundredth. $$ 12+9^{x}=122 $$

Solve each equation for the variable and check. \(2 \log x=\log 25\)

In \(3-14,\) write each exponential equation in logarithmic form. $$ 625^{\frac{3}{4}}=125 $$

In \(3-14,\) find the common logarithm of each number to the nearest hundredth. $$ 100 $$

In \(11-22,\) solve each equation for \(y\) in terms of \(x\) $$ x=8^{y} $$

In \(3-14,\) find the natural logarithm of each number to the nearest hundredth. $$ \frac{1}{e} $$

In \(3-14,\) solve each equation for the variable. Express each answer to the nearest hundredth. $$ 75-4^{b}=20 $$

Solve each equation for the variable and check. \(3 \ln x+\ln 24=\ln 3\)

In \(3-14,\) write each exponential equation in logarithmic form. $$ 0.001=100^{-\frac{3}{2}} $$

In \(3-14,\) find the common logarithm of each number to the nearest hundredth. $$ 0.1 $$

In \(11-22,\) solve each equation for \(y\) in terms of \(x\) $$ x=(0.1)^{y} $$

In \(15-20,\) evaluate each logarithm to the nearest hundredth. $$ \ln \frac{1}{2} $$

When Rita was five, she had \(\$ 1\) in her piggy bank. The next year she doubled the amount that she had in her piggy bank to \(\$ 2 .\) She decided that each year she would double the amount in her piggy bank. How old will Rita be when she has at least \(\$ 1,000\) in her piggy bank?

Find \(x\) to the nearest hundredth. \(\log x-2=\log 5\)

In \(15-23,\) evaluate each logarithm to the nearest hundredth. $$ \log 1,024 $$

In \(15-26,\) write each logarithmic equation in exponential form. $$ \log _{10} 100=2 $$

a. Write each expression as a single logarithm. b. Find the value of each expression. \(\log _{3} 1+\log _{3} 9\)

In \(11-22,\) solve each equation for \(y\) in terms of \(x\) $$ x=(0.2)^{y} $$

In \(15-20,\) evaluate each logarithm to the nearest hundredth. $$ \ln 5+\ln 7 $$

An investment of \(\$ 2,000\) receives 5\(\%\) interest annually. After how many years has the investment increased to at least \(\$ 2,500 ?\)

Find \(x\) to the nearest hundredth. \(\log x+\log (x+2)=\log 3\)

In \(15-23,\) evaluate each logarithm to the nearest hundredth. $$ \log 80 $$

In \(15-26,\) write each logarithmic equation in exponential form. $$ \log _{5} 125=3 $$

a. Write each expression as a single logarithm. b. Find the value of each expression. \(\log _{3} 27+\log _{3} 81\)

In \(11-22,\) solve each equation for \(y\) in terms of \(x\) $$ x=4^{-y} $$

In \(15-20,\) evaluate each logarithm to the nearest hundredth. $$ \frac{1}{2} \ln 3-\frac{1}{2} \ln 1 $$

When interest is compounded quarterly (4 times a year) at an annual rate of 6\(\%\) , the rate of interest for each quarter is \(\frac{0.06}{4}\) , and the number of times that interest is added in \(t\) years is 4\(t\) . After how many years will an investment of \(\$ 100\) compounded quarterly at 6\(\%\) annully be worth at least \(\$ 450 ?\) (Use the formula \(A_{n}=A_{0}\left(1+\frac{r}{n}\right)^{n t} . )\)